How do I bait the parrot?
After a short wiki check on the Zombie Parrot it seems that it chooses the plants absolutely at random. It also says that:
It steals plants like Bungee Zombies if it is not defeated in time.
From my personal experience I can say that it's (almost) impossible to tell which plant will it (try to) steal before it lands on it. I assume that you want to bait it into an Iceberg Lettuce only because it costs nothing, but I'm quite sure that it's impossible to force it to take the plant of your choice. But normally by the time you encounter them you have enough defense to kill them. Personally I had a Repeater and some other plants in each row which was enough to kill it before it got too far.
Possible strategies vs. Zombie Parrot:
If you see that you won't be able to kill him before he passes your attacking plants, you may want to use a Plant Food on a plant that attack the row in which the Parrot is flying at that moment. A good option would be to feed a Cabbage Pult, because it heavily attacks all zombies on the screen.
If you want to slow the game down a bit to let you gather more sun and not to lose a plant you may plant the Iceberg Lettuce somewhere and immediately feed it with Plant Food. It will freeze all zombies on the screen(pretty much the same as Ice Shroom from the first game).
I don't know if there is anything like Umbrella Leaf in the second game, but if I will find a defensive plant against Parrots I'll update my answer.
I've noticed the pat of butter from the corn catapult instantly kills the parrot...it also makes the seagull drop his zombie